Question

Building A and building B are 500 meters apart. There is no road between them, so to drive from building A to building B, it is necessary to first drive to building C and then to building B. About how much farther is it to drive than to walk directly from building A to building B? Round to the nearest whole number. A) 183 meters B) 250 meters C) 366 meters D) 683 meters

Answer 1

a)183

Explanation:

just took the test

Answer 2

Option A) 183 meters

Explanation:

see the attached figure to better understand the problem

step 1

Find the distance BC

we know that

In the right triangle ABC

`cos(60\°)=(BC)/(AB)` ----> adjacent side divided by the hypotenuse

Remember that

`cos(60\°)=1/2`

substitute the values

`1/2=(a)/(500)`

`a=250\ m`

step 2

Find the distance AC

In the right triangle ABC

`sin(60\°)=(AC)/(AB)` ----> opposite side divided by the hypotenuse

Remember that

`sin(60\°)=(√(3))/(2)`

substitute the values

`(√(3))/(2)=(b)/(500)`

`b=250√(3)= 433\ m`

step 3

Find the distance AC+CB

`433+250=683\ m`

Subtract the distance AB from 683 m

`683-500=183\ m`